Overview
In this chapter we discuss the general aspects of the longitudinal development of air showers and the effects of the primary energy and mass. These are based on the fundamental processes treated in detail in Chaps. 3, 4 and 5. However, the current chapter can in principle be studied without the full knowledge of the contents of the previous chapters, but some knowledge of hadronic and electromagnetic interactions is useful. Examples of simulated longitudinal shower profiles and the effect of the radiation length are presented. We then outline the longitudinal and lateral energy deposit profile of the different shower constituents in the atmosphere. This is followed by the definition of the shower rate attenuation and shower particle absorption. The absorption and attenuation lengths and coefficients are introduced, the relation of these quantities to the nucleon spectrum in the atmosphere and the mathematical expressions that link the observables are explained. Subsequently, the altitude and zenith angle dependence, and the influence of environmental parameters on the shower rate and the particle flux in showers are summarized. Experimental methods to access these quantities are discussed and data of the shower attenuation rate, the absorption of shower particles, the zenith angle dependence and of the environmental effects are discussed at some length. Finally, the concept of equal intensity cuts and distributions which offer deeper insight into the longitudinal development of showers are introduced and data samples presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Of particular interest are the energy dependent inelastic cross sections for collisions of nucleons, pions and other hadrons, such as nuclei, with nuclei of air constituents, \(\sigma^{N,A}_{\mathrm{inel}}, \ \sigma^{\pi,A}_{\mathrm{inel}}\), etc., where A stands for 14N or 16O.
- 2.
The energy dependence of the secondary particle multiplicity is discussed in Sect. 3.5.
- 3.
For a detailed discussion on the leading particle effect, elasticity and inelasticity see Sect. 3.8.
- 4.
In spite of the fact that muons do not generate a cascade themselves, but represent so-to-say an extension of the history of the hadron cascade into the deeper atmosphere where they exhibit a shower like behavior when analyzed with a detector array, we use the term hadron–muon cascade in place of hadron cascade and associated muon shower .
- 5.
This program system, called ASICO, was the forerunner of today’s widely used CORSIKA program (Capdevielle et al., 1992; Heck et al., 1998a, b; Heck and Knapp, 2002). The two programs have essentially identical structures, however, an extended choice of modern interaction models (event generators) is now available with CORSIKA (for details see Chap. 20).
- 6.
Different authors use different values for χ 0. In older work 36.66 g cm−2 was frequently used; today a value of 37.1 g cm−2 is recommended.
- 7.
In the literature there is no clear-cut terminology. Attenuation length as well as absorption length are used for shower rate attenuation and/or shower particle absorption, and likewise for Λ and λ.
- 8.
We disregard the steepening of the spectrum beyond the so-called knee.
- 9.
We write N instead of N e in this case since experimentally the distinction between the electron size, N e , and the total shower size, N, which includes all particles, is made only in a few experiments, e.g., in KASCADE (Antoni et al., 2003).
- 10.
Charmed particles are little affected by the changing density because of their very short mean life.
- 11.
It is assumed that the primary composition remains constant; if energy dependent it affects the shower development.
- 12.
Kaons affect the shower development alike but play an inferior role because they are much less abundant. Because of the very short mean life of charmed particles and the high production threshold energy their contribution to the high energy muon flux at ground level is essentially independent of zenith angle.
- 13.
For zenith angles \(\theta \geq (70^{\circ}-80^{\circ})\), depending on the accuracy required, the Chapman function must be used to compute the atmospheric column density along the trajectory correctly.
- 14.
The muon content in muon-poor showers amounts to about 1% or less of all the particles.
- 15.
Note that in this experiment the electron component can be separated from the bulk of all-charged particles.
References
Aglietta, M., et al.: Nucl. Instr. Meth., A 277, p. 23 (1989).
Aglietta, M., et al.: EAS-TOP Collaboration: PICRC, 2, p. 800 (1995).
Aglietta, M., et al.: PICRC, 6, p. 37 (1997).
Aglietta, M., et al.: Nucl. Phys. B (Proc. Suppl.), 75A, p. 222 (1999).
Aguirre, C., et al.: PICRC, 8, p. 208 (1977a).
Aguirre, C., et al.: PICRC, 8, p. 213 (1977b).
Aguirre, C., et al.: PICRC, 8, p. 107 (1979a).
Aguirre, C., et al.: J. Phys. G, 5, p. 139 (1979b).
Aguirre, C., et al.: J. Phys. G, 5, p. 151 (1979c).
Aminjeva, T.P., et al.: Izv. Akad. Nauk SSSR, Ser. Fiz., 33, p. 1508 (1969) (in Russian).
Antoni, T., et al.: Astropart. Phys., 19, p. 703 (2003).
Antonov, Yu.N., et al.: Sov. Phys. JETP, 5, p. 172 (1957).
Antonov, R.A., et al.: PICRC, 2, p. 96 (1960).
Antonov, R.A., et al.: Zh. Eksp. Teor. Fiz., 45, p. 1865 (1963).
Antonov, R.A., et al.: Sov. Phys. JETP, 18, p. 1279 (1964a).
Antonov, R.A., et al.: Sov. Phys. JETP, 19, p. 20 (1964b).
Antonov, R.A., et al.: Trudi, FIAN 26, p. 142 (1964c) (in Russian).
Antonov, R.A., et al.: PICRC, 6, p. 2194 (1971).
Antonov, R.A., et al.: Yadernaya Fiz., 18, p. 554 (1973) (in Russian).
Antonov, R.A.: Yadernaya Fiz., 19, p. 1053 (1974) (in Russian). Sov. J. Nucl. Phys., 19, p. 540 (1974).
Antonov, R.A. and I.P. Ivanenko: Yadernaya Fiz., 19, p. 869 (1974) (in Russian). Sov. J. Nucl. Phys., 19, p. 443 (1974).
Antonov, R.A., et al.: Sov. J. Nucl. Phys., 18, p. 285 (1974).
Antonov, R.A. and I.P. Ivanenko: PICRC, 8, p. 2708 (1975a).
Antonov, R.A. and I.P. Ivanenko: PICRC, 8, p. 2714 (1975b).
Antonov, R.A., et al.: PICRC, 9, p. 3360 (1975).
Antonov, R.A., et al.: PICRC, 8, p. 137 (1977).
Antonov, R.A., et al.: PICRC, 9, p. 258 (1979a).
Antonov, R.A., et al.: PICRC, 9, p. 263 (1979b).
Antonov, R.A., et al.: PICRC, 9, p. 269 (1979c).
Antonov, R.A., et al.: Izv. AN SSSR, Ser. Fiz., 44, p. 547 (Bull. USSR Acad. Sci. Phys. Ser.) (1980).
Antonov, R.A., et al.: PICRC, 6, p. 225 (1981).
Antonov, R.A., et al.: PICRC, 6, p. 52 (1983).
Antonov, R.A., et al.: Yadernaya Fiz., 40, p. 1222 (1984) (in Russian). Sov. J. Nucl. Phys., 40, p. 775 (1984).
Ashton, F., and R.B. Coats: J. Phys., A 1, p. 169 (1968).
Ashton, F., et al.: Acta Phys. Acad. Sci. Hung., 29, S3, p. 327 (1970).
Ashton, F., and A. Parvaresh: PICRC, 8, p. 2719 (1975).
Ashton, F., et al.: PICRC, 8, p. 2831 (1975).
Ashton, F., et al.: PICRC, 13, p. 238 (1979).
Auger, P.: Comptes Rendus Acad. Sci. Paris, 207, p. 907 (1938) (in French).
Auger, P., et al.: Comptes Rendus Acad. Sci. Paris, 206, p. 1721 (1938) (in French).
Auger, P., et al.: J. de Phys. et Radium, 10, p. 39 (1939a) (in French).
Auger, P., et al.: Comptes Rendus Acad. Sci. Paris, 208, p. 1641 (1939b) (in French).
Auger, P.: J. de Phys. et Radium, 1, p. 173 (1940) (in French).
Auger, P., and J. Daudin: Phys. Rev., 61, p. 91 (1942).
Auger, P., and J. Daudin: J. de Phys. et Radium, 6, p. 233 (1945) (in French).
Baltrusaitis, R.M., et al.: Phys. Rev. Lett., 52, p. 1380 (1984).
Bassi, P., et al.: Nuovo Cim., 9, p. 1037 (1952) (in Italian).
Bassi, P., et al.: Phys. Rev., 92, p. 441 (1953).
Bazarov, E.V., et al.: PICRC, 5, p. 32 (1981).
Bell, C.J., et al.: PICRC, 4, p. 2519 (1973).
Bell, C.J., et al.: J. Phys. A, 7, p. 990 (1974).
Bell, C.J.: J. Phys. G, 2, p. 867 (1976).
Bellandi, J., et al.: Nuovo Cim., 111 A, p. 149 (1998).
Bennett, S., et al.: J. Phys. Soc. Jpn., 17, Suppl. A III, p. 196 (1962).
Bergeson, H.E., et al.: PICRC, 8, p. 3059 (1975a).
Bergeson, H.E., et al.: PICRC, 8, p. 3064 (1975b).
Biehl, A.T., et al.: Phys. Rev., 76, p. 914 (1949).
Blatt, J.M.: Phys. Rev., 75, p. 1584 (1949).
Böhm, E., and M. Nagano: J. Phys. A, 6, p. 1262 (1973).
Böhm, E. and E. Steinmann: PICRC, 8, p. 294 (1979).
Bourdeau, M.F., et al.: J. Phys. G, 2, p. 57 (1976).
Bourdeau, M.F., et al.: J. Phys. G, 6, p. 401 (1980).
Bradt, H., et al.: PICRC, 2, p. 715 (1965).
Braun, I., et al.: Adv. Space Res., 43, p. 480 (2008).
Broadbent, D., et al.: Proc. Phys. Soc. A, 63, p. 864 (1950).
Brooke, G., et al.: Proc. Phys. Soc., 83, p. 853 (1964).
Brown, W.W., and A.S. McKay: Phys. Rev., 76, p. 1034 (1949).
Capdevielle, J.N.: Ph.D. Thesis, University of Paris, Paris (1972).
Capdevielle, J.N., and A. Cachon: J. Phys. G, 1, p. 120 (1975).
Capdevielle, J.N., and J. Procureur: J. Phys. G, 10, p. 705 (1984).
Capdevielle, J.N., et al.: The Karlsruhe EAS simulation code CORSIKA, KFK Report 4998 (1992).
Castagnoli, C., et al.: Nuovo Cim., 7, p. 307 (1950).
Catz, Ph., et al.: PICRC, 3, p. 1030 (1971).
Catz, Ph., et al.: PICRC, 12, p. 4329 (1975).
Chapman, S.: Proc. Roy. Soc. (Lond.), 43, p. 483 (1931).
Chilingarian, A., et al.: PICRC, 1, p. 240 (1999).
Chudakov, A.E., et al.: PICRC, 2, p. 50 (1960).
Ciampa, D., et al.: Proc. Astron. Soc. Aust., 6, p. 336 (1986).
Ciampa, D., and R.W. Clay: J. Phys. G, 14, p. 787 (1988).
Citron, A.: Zeitschrift für Naturforschung, 7a, p. 712 (1952).
Citron, A., and G. Stiller: Nuovo Cim., Suppl. 8, p. 675 (1958).
Clark, G.W.: Phys. Rev., 108, p. 450 (1957).
Clark, G., et al.: Nature, 180, p. 353 (1957).
Clark, G., et al.: Nuovo Cim., Suppl. 8, p. 623 (1958).
Clark, G.W., et al.: Phys. Rev., 122, p. 637 (1961).
Clark, G., et al.: PICRC, 4, p. 65 (1963).
Clay, R.W., and P.R. Gerhardy: J. Phys. G, 7, p. L33 (1981a).
Clay, R.W., and P.R. Gerhardy: Nuovo Cim., 4 C, p. 26 (1981b).
Clay, R.W., and P.R. Gerhardy: Aust. J. Phys., 35, p. 59 (1982).
Cocconi, G. and V. Tongiorgi: Phys. Rev., 70, p. 850 (1946).
Cocconi, G., et al.: Phys. Rev., 70, p. 846 (1946).
Cocconi, G.: Phys. Rev., 76, p. 984 (1949a).
Cocconi, G.: Phys. Rev., 75, p. 1074 (1949b).
Cocconi Tongiorgi, V.: Phys. Rev., 76, p. 192 (1949).
Cocconi, G., and V. Cocconi Tongiorgi: Phys. Rev., 76, p. 318 (1949a).
Cocconi, G., and V. Cocconi Tongiorgi: Phys. Rev., 75, p. 1058 (1949b).
Cocconi, G., et al.: Phys. Rev., 75, p. 1063 (1949).
Cocconi, G.: Handbuch der Physik, S. Flügge, ed., Kosmische Strahlung, XLVI/I, p. 215, Springer Verlag, Berlin (1961).
Coxell, H., et al.: Proc. Phys. Soc., 81, p. 604 (1963).
Cranshaw, T.E., et al.: Phil. Mag., 2, p. 891 (1957).
Cranshaw, T.E., et al.: Phil. Mag., 3, p. 811 (1958a).
Cranshaw, T.E., et al.: Nuovo Cim., Suppl. 8, p. 567 (1958b).
Danilova, T.V., et al.: PICRC, 8, p. 129 (1977).
Daudin, J.: J. Phys. et Radium, 6, p. 302 (1945) (in French).
Daudin, J., and A. Daudin: J. de Phys. et Radium, 10, p. 394 (1949) (in French).
Daudin, A., and J. Daudin: J. Atmos. Terr. Phys. 3, p. 245 (1953a) (in French).
Daudin, A., and J. Daudin: Bagneres-de-Bigorre Conf. J. Phys. Radium 14, p. 169 (1953b) (in French).
Daudin, A., et al.: Nuovo Cim., 3, p. 1017 (1956) (in French).
De Beer, J.F., et al.: Phil. Mag., 7, p. 499 (1962).
Dedenko, L.G.: PICRC, 8, p. 2857 (1975).
Delvaille, J., et al.: PICRC, 2, p. 79 (1960).
Deutschmann, M.: Z. Naturforschung, 2a, p.61 (1947).
Diminstein, O.S., et al.: PICRC, 12, p. 4325 (1975).
Diminstein, O.S., et al.: PICRC, 8, p. 154 (1977).
Diminstein, O.S., et al.: PICRC, 8, p. 122 (1979).
Dremin, I.M., et al.: PICRC, 8, p. 314 (1985).
Efimov, N.N.: Ph.D. Thesis, Moscow State University, Moscow (1967).
Euler, H.: Z. Phys., 116, p. 73 (1940).
Farley, F.J.M., and J.R. Storey: Proc. Phys. Soc. A, 67, p. 996 (1954).
Farley, F.J.M., and J.R. Storey: Proc. Phys. Soc. Lond. B, 70, p. 840 (1957).
Firkowski, R., et al.: PICRC, 2, p. 694 (1965).
Firkowski, R., et al.: Inst of Nucl. Research, Warsaw, Poland, Report No. 803/VI-PH (1967).
Fukui, S., et al.: Prog. Theor. Phys. Jpn., 16, p. 1 (1960).
Galbraith, W.: Extensive Air Showers, Butterworths Scientific Publications, London (1958).
Gawin, J., et al.: Proceeding VI. Interamerican Seminar on Cosmic Rays, La Paz, Bolivia 3, p. 723 (1970).
Genannt, R., and H. Pilkuhn: PICRC, 4, p. 2434 (1973).
Goodman, J.A., et al.: Phys. Rev. D, 29, p. 1043 (1982).
Goorevich, L., and L.S. Peak: J. Phys. A, 7, p. 1777 (1974).
Greisen, K.: Progress in Cosmic Ray Physics, North Holland, Amsterdam, Vol. 3, p. 1 (1956).
Greisen, K.: Annual Review of Nuclear Science, Annual Reviews Inc., Palo Alto, CA, 10, p. 63 (1960).
Grieder, P.K.F.: Rivista del Nuovo Cim., 7, p. 1 (1977).
Grieder, P.K.F.: PICRC, 9, p. 184 (1979a).
Grieder, P.K.F.: PICRC, 9, p. 178 (1979b).
Grieder, P.K.F.: Nuovo Cim., 84 A, p. 285 (1984).
Grieder, P.K.F.: Proceedings of Japan – US Seminar on Cosmic Ray Muon and Neutrino Physics/Astrophysics Using Deep Underground/Underwater Detectors, Institute for Cosmic Ray Research, University of Tokyo, Tokyo, p. 183 (1986).
Gross, B: Zeitschr. f. Physik, 83, p. 214 (1933).
Guseva, V.V., et al.: Sov. Phys. JETP, 35(8), p. 577 (1959).
Hara, T., et al.: PICRC, 6, p. 52 (1981a).
Hara, T., et al.: PICRC, 11, p. 250 (1981b).
Hara, T., et al.: Phys. Rev. Lett., 50, p. 2058 (1983a).
Hara, T., et al.: PICRC, 11, p. 281 (1983b).
Hasegawa, H., et al.: J. Phys. Soc. Jpn., 17, Suppl. A-III, p. 189 (1962).
Hayakawa, S.: Cosmic Ray Physics, Wiley – Interscience, New York (1969).
Hazen, W.E., et al.: Phys. Rev., 93, p. 578 (1954).
Heck, D., et al.: Report FZKA 6019, Forschungszentrum Karlsruhe (1998a).
Heck, D., et al.: Report FZKA 6097, Forschungszentrum Karlsruhe (1998b).
Heck, D., and J. Knapp: Extensive Air Shower Simulation with CORSIKA: A User’s Guide, Forschungszentrum Karlsruhe, Germany. Version 6.018 October 1 (2002).
Heck, D., and J. Knapp: Extensive Air Shower Simulation with CORSIKA: A User’s Guide, Forschungszentrum Karlsruhe, Germany; Version 6.500, March 6, (2006). Updated version, see CORSIKA.
Heintze, J., et al.: Nucl. Instr. Meth., A277, p. 29 (1989a).
Heintze, J., et al.: Proceedings of KFK Workshop, Burg Liebenzell, October (1989b).
Hersil, J., et al.: J. Phys. Soc. Jpn., 17, Suppl. A-III, p. 243 (1962).
Hilberry, N.: Phys. Rev., 60, p. 1 (1941).
Hinotani, K., et al.: PICRC, 4, p. 277 (1963).
Hochart, J.P., et al.: PICRC, 8, p. 2822 (1975).
Hochart, J.P.: Ph. D. Thesis, University of Paris, Paris VI (1976).
Hodson, A.L.: Proc. Phys. Soc. A, 64, p. 1061 (1951).
Hodson, A.L.: Proc. Phys. Soc. A, 65, p. 702 (1952).
Hodson, A.L.: Proc. Phys. Soc. A 66, p. 49 (1953a).
Hodson, A.L.: Proc. Phys. Soc. A 66, p. 65 (1953b).
Honda, M., et al.: Phys. Rev. Lett., 70, p. 525 (1993).
Proceedings, ISVHECRI (International Symposium on Vey High Energy Cosmic Ray Interactions), Paris, France, September 1–6 (2008).
Janossy, L.: Cosmic Rays, Oxford University Press, Oxford (1948).
Janossy, L., et al.: Nuovo Cim., Suppl., VIII, p. 701 (1958).
Kakimoto, F., et al.: PICRC, 11, p. 254 (1981).
Kakimoto, F., et al.: Nucl. Instr. Meth. A, 373, p. 282 (1996).
Kalmykov, N.N., et al.: PICRC, 6, p. 2074 (1971).
Kalmykov, N.N., et al.: PICRC, 4, p. 2633 (1973).
Kalmykov, N.N., et al.: Nucl. Phys. B, (Proc. Suppl.), 52, p. 17 (1997).
Keilhauer, B., et al.: Preprint, FZK, November (2005).
Khristiansen, G.B., et al.: PICRC, 8, p. 148 (1977).
Khristiansen, G.B.: Cosmic Rays of Superhigh Energies. Verlag Karl Thiemig, München (1980).
Kirov, I.N., et al.: PICRC, 2, p. 109 (1981).
Kohlhörster, W., et al.: Naturwissenschaften, 26, p. 576 (1938).
Konishi, E., et al.: J. Phys. G, 17, p. 719 (1991).
Kozlov, V.I., et al.: PICRC, 4, p. 2588 (1973).
Krasilnikov, D.D.: after Bennett, (1962).
Kraybill, H.L.: Phys. Rev., 73, p. 632 (1948).
Kraybill, H.L.: Phys. Rev., 76, p. 1092 (1949).
Kraybill, H.L.: Phys. Rev., 86, p. 590 (1952).
Kraybill, H.L.: Phys. Rev., 93, p. 1360 (1954a).
Kraybill, H.L.: Phys. Rev., 93, p. 1362 (1954b).
Kulikov, G.V., et al.: PICRC, 2, p. 85 (1960).
Landau, L.D., and I.Ya. Pomeranchuck: Dokl. Akad. Nauk. SSSR, 92, p. 535 (1953a).
Landau, L.D., and I.Ya. Pomeranchuck: Dokl. Akad. Nauk. SSSR, 92, p. 735 (1953b).
La Pointe, M., et al.: Can. J. Phys., 46, p. 68 (1968).
Lewis, H.W.: Phys. Rev., 73, p. 1341 (1948).
Linsley, J.: PICRC, 5, p. 3207 (1973).
Linsley, J.: PICRC, 12, p. 89 (1977).
Linsley, J.: PICRC, 6, p. 246 (1981).
Linsley, J.: PICRC, 7, p. 163 (1985).
Loverdo, A., and J. Daudin: J. de Phys. et Radium, 9, p. 134 (1948).
MacLeod, G.R.: Nuovo Cim., 3, p. 118 (1956).
Malos, J.: PICRC, 2, p. 84 (1960).
Maze, R., et al.: Phys. Rev., 73, p. 418 (1948).
Maze, R.: Acta Phys. Acad. Sci. Hung., 29, S3, p. 685 (1970).
McComb, T.J.L., et al.: PICRC, 9, p. 126 (1979a).
McComb, T.J.L., et al.: J. Phys. G, 5, p. 1613 (1979b).
Mielke, H.H., et al.: PICRC, 4, p. 155 (1993).
Mielke, H.H., et al.: J. Phys. G, 20, p. 637 (1994).
Migdal, A.B.: Phys. Rev., 103, p. 1811 (1956).
Millar, D.D.: Proc. Roy. Irish Acad., 54, p. 115 (1951).
Mills, M.M.: Phys. Rev., 74, p. 1555 (1948).
Miyake, S.: Prog. Theor. Phys., 20, p. 844 (1958).
Miyake, S.: J. Phys. Soc. Jpn., 17, Suppl. A-III, p. 291 (1962).
Miyake, S., et al.: Can. J. Phys., 46, p. S21 (1968).
Miyake, S., et al.: PICRC, 7, p. 2748 (1971).
Miyake, S., et al.: PICRC, 13, p. 171 (1979).
Mizumoto, Y., et al.: PICRC, 9, p. 116 (1979).
Molière, G.: Vorträge über Kosmische Strahlung, 2. Auflage (in German), ed. W. Heisenberg, p. 446 Springer, Berlin (1953).
Nagano, M., et al.: J. Phys. G, 10, p. L235 (1984a).
Nagano, M., et al.: J. Phys. G, 10, p. 1295 (1984b).
Nagano, M., et al.: J. Phys. G, 18, p. 423 (1992).
NEEDS Workshop: Informal meeting on “Needs for Accelerator Experiments for the Understanding of High Energy Extensive Air Showers”, R. Engel, A. Haungs, L. Jones, and H. Rebel, initiators, April 18–20 (2002). Contributions available as PDF-Files at http://www-ik.fzk.de/ needs/needs_1c.htm
Nikolsky, S.I.: Usp. Fiz. Nauk 135, p. 545 (1981a).
Nikolsky, S.I.: Sov. Phys. Uspekhi 24, p. 925 (1981b).
Nishimura, J.: Handbuch der Physik, 46/2, p. 1, Springer Verlag, Berlin (1967).
Ogio, S., et al.: Astrophys. J., 612, p. 268 (2004).
Ohta, K., et al.: PICRC, 13, p. 177 (1979).
Ostapchenko, S.: Nucl. Phys. B (Proc. Suppl.), 151, p. 143 (2006a).
Ostapchenko, S.: Nucl. Phys. B (Proc. Suppl.), 151, p. 147 (2006b).
Ostapchenko, S.: astro-ph/0610788 (2006c).
Ostapchenko, S.: Phys. Lett. B, 636, p. 40 (2006d).
Pattison, B., et al. (Eds.): Very High Energy Cosmic Ray Interactions. Proceedings of the 12th International Symposium on Very High Energy Cosmic Ray Interactions, Geneva, Switzerland 15–20 July 2002. Nuclear Physics B (Proc. Suppl.) 122 (2003) (487p.).
Popova, L., and J. Wdowczyk: PICRC, 8, p. 2883 (1975).
Procureur, J., et al.: PICRC, 8, p. 2878 (1975).
Rao, M.S.V., and B.V. Sreekantan: Extensive Air Showers, World Scientific, Singapore (1998).
Risse, M., and D. Heck: Astropart. Phys., 20, p. 661 (2004).
Rossi, B.: PICRC, 2, p. 18 (1960).
Sakaki, N.: Ph.D. Thesis, Department of Physics, University of Yamanashi , Kofu, Japan (2003).
Samorski, M.: Dissertation, University of Kiel, Kiel (1973).
Schopper, E.: Handbuch der Physik, S. Flügge, ed., 46/2, p. 372, Springer Verlag, Berlin (1967).
Sciutto, S.J.: http://www.fisica.unlp.edu.ar/auger/aires/ AIRES, version 2.6.0 (2002).
Sciutto, S.J.: PICRC, 7, p. 9 (2005).
Sokolsky, P.: Introduction to Ultrahigh Energy Cosmic Ray Physics, Frontiers in Physics, Vol. 76, Addison-Weskey Publishing Co., New York (1989).
Suga, K., et al.: PICRC, 13, p. 142 (1979).
Suri, A.N.: PICRC, 2, p. 751 (1965).
Tan, Y.H., et al.: ICR-Report 99-82-2, Institute for Cosmic Ray Research, University of Tokyo, Tokyo (1982).
Tennent, R.M.: Proc. Phys. Soc., 92, p. 622 (1967).
Treat, J.E., and K.I. Greisen: Phys. Rev., 74, p. 414 (1948).
Tsai, Y.S.: Rev. Mod. Phys., 46, p. 815 (1974).
Vernov, S.N., et al.: Can. J. Phys., 46, p. 197 (1968).
Wdowczyk, J. and A.W. Wolfendale: Nature 236, p. 29 (1972).
Williams, R.W.: Phys. Rev., 74, p. 1689 (1948).
Wolfendale, A.W.: Cosmic Rays at Ground Level. The Institute of Physics, London (1973).
Yakovlev, V.I.: Nucl. Phys. B (Proc. Suppl.), 122, p. 201 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Grieder, P.K. (2010). Longitudinal Development and Equal Intensity Distributions. In: Extensive Air Showers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76941-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-76941-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76940-8
Online ISBN: 978-3-540-76941-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)